In Kasese, Uganda, a man distributes newspapers with a title about the Ebola virus outbreak, on August 1, 2012. The Ugandan president has called on people to limit physical contact with each other, after the death toll of a deadly outbreak of the Ebola virus climbed to 18.

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Perhaps 1,850 people have been diagnosed with Ebola hemorrhagic fever since the virus was first identified 36 years ago in the Democratic Republic of Congo. (To put that number in perspective, more than 24,000 people fall ill from tuberculosis each day.) Still, Ebola has a grip on the public imagination that far exceeds the danger it actually poses — in part because of those 1,850 sick people, some 1,200 went on to die. And the deaths are rarely easy — Ebola can cause severe fever, muscle pain, weakness, vomiting, diarrhea and unstoppable bleeding. There is no treatment and no vaccine.

That’s why the latest Ebola outbreak in western Uganda, which has involved at least 20 cases and 14 deaths so far, has received so much attention. According to the World Health Organization (WHO), the outbreak originated in a family in Nyanswiga village in Uganda’s Kibaale district, 140 miles (225 km) west of Kampala, the capital. Such rural outbreaks are not unusual for Ebola — like many emerging infectious diseases, including HIV, it first jumped from primates like gorillas and chimpanzees to human beings, and outbreaks often begin with sick animals. It’s not surprising then that the first infections would often take place in the African countryside, where the hunting and consumption of wild animals is not uncommon, as I discovered when I visited Cameroon for a TIME story last year.

What’s got people worried in this case is that one infected patient managed to travel to a hospital in Uganda’s capital, Kampala, a city of 1.5 million people with air connections to the rest of Africa and the world. Although there has been no evidence yet that Ebola is actively spreading in the city, Kampala residents are, to put it simply, freaked out — so much so that people immediately fled the hospital once word spread that an Ebola patient was being treated there. Ugandan President Yoweri Museveni also raised alarm bells when he called on citizens to avoid physical contact to prevent transmission of the disease:

Ebola spreads by contact. When you contact each other physically then Ebola spreads through sweat, through saliva in case you kiss, blood (exchange of blood), vomiting in case you touch the vomit of somebody who is sick or diarrhea, urine, sexual fluids, etc., all those transmit Ebola. Fortunately it seems Ebola does not spread through air (through breathing); it spreads through contact.

But unless the virus somehow spreads from the Kampala hospital into the general population, the virus likely poses little threat to urban Ugandans — and even less to the rest of the world. That’s because as frightening as Ebola is, transmission requires direct contact with infected bodily fluids, including blood or saliva. It can’t be transmitted through the air like the flu or SARS. Unlike HIV, which is also passed through bodily fluids, Ebola makes the infected so obviously sick so soon that there’s little chance transmission could happen in secret. The most at-risk group for secondary Ebola infections is actually health care workers, which is why the 20 doctors and nurses who made the journey with the infected patient from Kibaale are in quarantine, just in case they too contracted the disease.

The presence of Ebola in a major African capital should still raise worries, however. New diseases begin in rural areas, where humans and wild animals — especially primates that are genetically closer to human beings — interact. But without roads and air travel, those viruses will mostly stay there. HIV was active among people in Central Africa for decades before it was able to spread to the rest of the world, thanks largely to air travel. The same thing happened with SARS in 2003: though the virus emerged in the marketplaces of southern China, where everything from wild civet cats to snakes are on the menu, it didn’t spread around the world until sick patients made it to Hong Kong, one of the busiest airports in the world.

Ebola has had decades to try to make it out of Africa and establish itself as a truly global threat. Thankfully for the rest of us, it hasn’t succeeded, and it seems unlikely to do so, barring some mutation in the virus that makes it more portable. But new viruses are always emerging in hot spots like Central Africa, places that are now perhaps just 24 hours’ travel from the U.S. (Remember Contagion?) Eventually one of them may well make it to the rest of the world — and the first stages may well resemble the Ebola outbreak hitting Uganda.